On Queues with Interruptions and Repeat or Resumption of Service

This thesis entitled' On Queues with Interruptions and Repeat or Resumption of Service' introduces several new concepts into queues with service interruption. It is divided into Seven chapters including an introductory chapter. The following are keywords that we use in this thesis: Phase type (PH) distribution, Markovian Arrival Process (MAP), Geometric Distribution, Service Interruption, First in First out (FIFO), threshold random variable and Super threshold random variable. In the second chapter we introduce a new concept called the 'threshold random variable' which competes with interruption time to decide whether to repeat or resume the interrupted service after removal of interruptions. This notion generalizes the work reported so far in queues with service interruptions. In chapter 3 we introduce the concept of what is called 'Super threshold clock' (a random variable) which keeps track of the total interruption time of a customer during his service except when it is realized before completion of interruption in some cases to be discussed in this thesis and in other cases it exactly measures the duration of all interruptions put together. The Super threshold clock is OIl whenever the service is interrupted and is deactivated when service is rendered. Throughout this thesis the first in first out service discipline is followed except for priority queues.

Impact of Self-generation of Priorities and Non-preemptive Service in Single/Multiserver Queues

In this thesis we have studied a few models involving self-generation of priorities. Priority queues have been extensively discussed in literature. However, these are situations involving priority assigned to (or possessed by) customers at the time of their arrival. Nevertheless, customers generating into priority is a common phenomena. Such situations especially arise at a physicians clinic, aircrafts hovering over airport running out of fuel but waiting for clearance to land and in several communication systems. Quantification of these are very little seen in literature except for those cited in some of the work indicated in the introduction. Our attempt is to quantify a few of such problems. In doing so, we have also generalized the classical priority queues by introducing priority generation ( going to higher priorities and during waiting). Systematically we have proceeded from single server queue to multi server queue. We also introduced customers with repeated attempts (retrial) generating priorities. All models that were analyzed in this thesis involve nonpreemptive service. Since the models are not analytically tractable, a large number of numerical illustrations were produced in each chapter to get a feel about the working of the systems.

Proposta de um algoritmo híbrido de agendamento de grants baseado na priorização de filas para gerenciamento de recursos em WDM-PONs

As Redes Ópticas Passivas (Passive Optical Networks - PONs) vêm experimentando um sólido crescimento nas últimas décadas por terem sido concebidas como uma excelente alternativa para a solução de um dos maiores problemas para as redes de telecomunicações: o gargalo nas redes de acesso. A próxima geração desta tecnologia, as chamadas Next Genaration PONs (NG-PON), surgem como consequência da evolução das tecnologias ópticas e oferecem suporte aos serviços de próxima geração, melhorando os parâmetros de desempenho das TDM-PONs e inclusive aumentando a área de cobertura destas redes. Esta expansão geográfica beneficia as empresas de telecomunicações que passam a focar seus esforços na simplificação de suas infra-estruturas através da unificação das redes metropolitanas, de acesso e de backhaul, reduzindo a quantidade de nós e, consequentemente, de custos operacionais e financeiros. Trata-se de uma significativa mudança no cenário das redes de acesso que passam a ter grandes distâncias entre as Optical Network Units (ONUs) e o Central Office (CO) e uma imensa variedade de serviços, tornando fundamental a presença de algoritmos de agendamento capazes de gerenciar todos os recursos compartilhados de forma eficiente, ao mesmo tempo que garantem controle e justeza na alocação dinâmica dos tráfegos upstream e downstream. É a partir deste contexto que esta dissertação tem como objetivo geral apresentar a proposta de um algoritmo híbrido de agendamento de grants baseado na priorização de filas (Hybrid Grant Scheduler based on Priority Queuing – HGSPQ), que além de gerenciar todos os recursos em WDM-PONs, busca oferecer eficiência e controle ao Optical Line Terminal (OLT) no agendamento dinâmico dos tráfegos. Os resultados apresentados foram extraídos de cenários desenvolvidos em ambiente de simulação computacional e se baseiam nas métricas de atraso e vazão para avaliação de seu desempenho. Também será avaliado como a quantidade de recursos no OLT interfere nestas métricas.

Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues

In the Hammersley-Aldous-Diaconis process, infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x, whose nearest neighbor to the right is at y, jumps at rate y - x to a position uniformly distributed in the interval (x, y). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows. First, a stationary M/M/1 queue is constructed as a function of two homogeneous Poisson processes, the arrivals with rate, and the (attempted) services with rate rho > lambda Then put first class particles at the instants of departures (effective services) and second class particles at the instants of unused services. The procedure is generalized for the n-class case by using n - 1 queues in tandem with n - 1 priority types of customers. A multi-line process is introduced; it consists of a coupling (different from Liggett's basic coupling), having as invariant measure the product of Poisson processes. The definition of the multi-line process involves the dual points of the space-time Poisson process used in the graphical construction of the reversed process. The coupled process is a transformation of the multi-line process and its invariant measure is the transformation described above of the product measure.

Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

Queues with retrial/self-generation of priorities /postponement of work and some related reliability problems

Application of Queueing theory in areas like Computer networking, ATM facilities, Telecommunications and to many other numerous situation made people study Queueing models extensively and it has become an ever expanding branch of applied probability. The thesis discusses Reliability of a ‘k-out-of-n system’ where the server also attends external customers when there are no failed components (main customers), under a retrial policy, which can be explained in detail. It explains the reliability of a ‘K-out-of-n-system’ where the server also attends external customers and studies a multi-server infinite capacity Queueing system where each customer arrives as ordinary but can generate into priority customer which waiting in the queue. The study gives details on a finite capacity multi-server queueing system with self-generation of priority customers and also on a single server infinite capacity retrial Queue where the customer in the orbit can generate into a priority customer and leaves the system if the server is already busy with a priority generated customer; else he is taken for service immediately. Arrival process is according to a MAP and service times follow MSP.

Queues with Customer Induced Interruption

In this thesis we have introduced and studied the notion of self interruption of service by customers. Service interruption in queueing systems have been extensively discussed in literature (see, Krishnamoorthy, Pramod and Chakravarthy [38]) for the most recent survey. So far all work reported deal with cases in which service interruptions are generated by sources other than customers. However, there are situations where interruptions are due to the customers rather than the system. Such situations are especially arise at doctors clinic, banks, reservation counter etc. Our attempt is to quantify a few of such problems. Systematically we have proceed from single server queue (in Chapter 2) to multi-server queues (Chapter 3). In Chapte 4, we have studied a very general multiserver queueing model with service interruption and protection of service phases. We also introduced customer interruption in a retrial setup (in Chapter 5). All models (from Chapter 2 to Chapter 4) that were analyzed involve 'non-preemptive priority' for interrupted customers where as in the model discussed in Chapter 5 interruption of service by customers is not encouraged. So the interrupted customers cannot access the server as long as there are primary customers in the system. In Chapter 5 we have obtained an explicit expression for the stability condition of the system. In all models analyzed in this thesis, we have assumed that no more than one interruption is allowed for a customer while in service. Since the models are not analytically tractable, a large number of numerical illustrations were given in each chapter it illustrate the working of the systems. We can extend the models discussed in this thesis to several directions. For example some of the models can be analyzed with both server induced and customer induced interruptions the results for which are not available till date. Another possible extension of work is to the case where there is no bound on the number of interruptions a customer is permitted to have before service completion. More complex is the case where a customer is permitted to have a nite number (K ≥ 2) of We can extend the models discussed in this thesis to several directions.

Congestion pricing by priority auction

This paper analyzes a communication network facing users with a continuous distribution of delay cost per unit time. Priority queueing is often used as a way to provide differential services for users with different delay sensitivities. Delay is a key dimension of network service quality, so priority is a valuable resource which is limited and should to be optimally allocated. We investigate the allocation of priority in queues via a simple bidding mechanism. In our mechanism, arriving users can decide not to enter the network at all or submit an announced delay sensitive value. User entering the network obtains priority over all users who make lower bids, and is charged by a payment function which is designed following an exclusion compensation principle. The payment function is proved to be incentive compatible, so the equilibrium bidding behavior leads to the implementation of "cµ-rule". Social warfare or revenue maximizing by appropriately setting the reserve payment is also analyzed.

Randomized Push-Out Mechanisms in Priority Queuing and their Probability Characteristics

2002 Mathematics Subject Classification: 60K25.

Segurança no circo : questão de prioridade = Circus safety: a priority issue

Universidade Estadual de Campinas . Faculdade de Educação Física

Definition of priority areas for forest conservation through the ordered weighted averaging method

The general objective of this study was to evaluate the ordered weighted averaging (OWA) method, integrated to a geographic information systems (GIS), in the definition of priority areas for forest conservation in a Brazilian river basin, aiming at to increase the regional biodiversity. We demonstrated how one could obtain a range of alternatives by applying OWA, including the one obtained by the weighted linear combination method and, also the use of the analytic hierarchy process (AHP) to structure the decision problem and to assign the importance to each criterion. The criteria considered important to this study were: proximity to forest patches; proximity among forest patches with larger core area; proximity to surface water; distance from roads: distance from urban areas; and vulnerability to erosion. OWA requires two sets of criteria weights: the weights of relative criterion importance and the order weights. Thus, Participatory Technique was used to define the criteria set and the criterion importance (based in AHP). In order to obtain the second set of weights we considered the influence of each criterion, as well as the importance of each one, on this decision-making process. The sensitivity analysis indicated coherence among the criterion importance weights, the order weights, and the solution. According to this analysis, only the proximity to surface water criterion is not important to identify priority areas for forest conservation. Finally, we can highlight that the OWA method is flexible, easy to be implemented and, mainly, it facilitates a better understanding of the alternative land-use suitability patterns. (C) 2008 Elsevier B.V. All rights reserved.

Biogeographical concordance and efficiency of taxon indicators for establishing conservation priority in a tropical rainforest biota

Prioritizing areas for conservation requires the use of surrogates for assessing overall patterns of biodiversity. Effective surrogates will reflect general biogeographical patterns and the evolutionary processes that have given rise to these and their efficiency is likely to lie influenced by several factors, including the spatial scale of species turnover and the overall congruence of the biogeographical history. We examine patterns of surrogacy for insects, snails, one family of plants and vertebrates from rainforests of northeast Queensland, an area characterized by high endemicity and an underlying history of climate-induced vicariance. Nearly all taxa provided some level of prediction of the conservation values For others. However, despite an overall correlation of the patterns of species richness and complementarity, the efficiency of surrogacy was highly asymmetric.. snails and insects were strong predictors of conservation priorities for vertebrates, but not vice versa. These results confirm predictions that taxon surrogates can be effective in highly diverse tropical systems where there is a strong history of vicariant biogeography, but also indicate that correlated patterns for species richness and/or complementarity do not guarantee that one taxon will be efficient as a surrogate for another. In our case, the highly diverse and narrowly distributed invertebrates were more efficient as predictors than the less diverse and more broadly distributed vertebrates.

Static-priority scheduling of sporadic messages on a wireless channel

Consider the problem of scheduling sporadic messages with deadlines on a wireless channel. We propose a collision-free medium access control (MAC) protocol which implements static-priority scheduling and present a schedulability analysis technique for the protocol. The MAC protocol allows multiple masters and is fully distributed; it is an adaptation to a wireless channel of the dominance protocol used in the CAN bus. But unlike that protocol, our protocol does not require a node having the ability to receive an incoming bit from the channel while transmitting to the channel.

Evaluating P-NET message's response time with fixed priority queuing at application process level

P-NET is a multi-master fieldbus standard based on a virtual token passing scheme. In P-NET each master is allowed to transmit only one message per token visit. In the worst-case, the communication response time can be derived considering that, in each token cycle, all stations use the token to transmit a message. In this paper, we define a more sophisticated P-NET model, which considers the actual token utilisation. We then analyse the possibility of implementing a local priority-based scheduling policy to improve the real-time behaviour of P-NET.

Adding local priority-based dispatching mechanisms to P-NET networks: a fixed priority approach

In this paper we address the real-time capabilities of P-NET, which is a multi-master fieldbus standard based on a virtual token passing scheme. We show how P-NET’s medium access control (MAC) protocol is able to guarantee a bounded access time to message requests. We then propose a model for implementing fixed prioritybased dispatching mechanisms at each master’s application level. In this way, we diminish the impact of the first-come-first-served (FCFS) policy that P-NET uses at the data link layer. The proposed model rises several issues well known within the real-time systems community: message release jitter; pre-run-time schedulability analysis in non pre-emptive contexts; non-independence of tasks at the application level. We identify these issues in the proposed model and show how results available for priority-based task dispatching can be adapted to encompass priority-based message dispatching in P-NET networks.